visigence-igad 1.0.1

Information-Geometric Anomaly Detection via Fisher–Rao Scalar Curvature

Verified

IGAD-VER-1.0.0 was validated on GitHub Actions at commit 81dd1eb4540643083854232d9645f6add4150512. The PyPI release was built from commit 156160d59f288d11451895ecb8c234ff7ef9c895. The validation run executed on GitHub-hosted Linux runners and completed successfully across Python 3.10, 3.11, and 3.12, producing separate test-report artifacts for each runtime.

View the exact GitHub Actions validation run.

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What is IGAD?

IGAD detects anomalies by measuring scalar curvature on the statistical manifold of an exponential family. Instead of comparing moments directly, it contracts the full third cumulant tensor against the Fisher–Rao metric, extracting shape information that no single moment captures.

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Experimental Results

All results are reproducible via experiments/.

Easy Case — Gamma vs Gamma

Different variance.

Method	AUC-ROC
IGAD (curvature)	1.0000
Variance shift	1.0000
Skewness shift	0.9834
Mean shift	0.8150

IGAD achieves perfect separation. Variance shift matches it, so this regime does not isolate the geometric advantage.

Hard Case — Matched Mean and Variance

Same mean = 4.0. Same variance = 2.0. Gamma vs LogNormal.
Evaluation: n = 200, 5 seeds.

Method	Mean AUC	± Std
IGAD (curvature)	0.6542	0.0469
MLE skewness (control)	0.6016	0.0382
Raw skewness	0.6794	0.0722
Mean shift	0.5240	0.0618
Variance shift	0.5818	0.0266

IGAD beats the MLE-skewness control by +0.053, showing that scalar curvature contributes signal beyond MLE efficiency alone.

Scaling with Batch Size

Seed = 42.

n	IGAD	MLE-skew	Gap
100	0.5704	0.5764	−0.006
200	0.6838	0.6098	+0.074
500	0.6748	0.5846	+0.090
1000	0.7892	0.8214	−0.032

The geometric advantage is strongest at n = 200–500. At n = 1000, model misspecification degrades the curvature signal.

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Honest Limitations

• Model specification required: IGAD needs a correctly chosen exponential family.
• 1D families such as Poisson, Exponential, and Bernoulli are flat, with R = 0.
• Model-free methods can dominate at n > 500 under misspecification.
• Computational cost is O(d³) tensor contractions per evaluation.

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Falsifiable Claim

IGAD's advantage over MLE-derived skewness, using the identical MLE fit but discarding the curvature tensor, shows that the full contraction ‖T‖²_g extracts shape information not captured by any single moment, raw or MLE-fitted.

This claim is supported in the tested regime n = 200–500 and remains falsifiable outside that regime.

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Verified Test Suite

• Validated commit: 81dd1eb4540643083854232d9645f6add4150512
• Release commit: 156160d59f288d11451895ecb8c234ff7ef9c895
• Release tag: IGAD-VER-1.0.0
• Python versions: 3.10, 3.11, 3.12
• Result: 54/54 tests passed
• Evidence: GitHub Actions validation run

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Install

pip install visigence-igad